Convenient stability criteria for difference approximations of hyperbolic initialboundary value problems
Authors:
Moshe Goldberg and Eitan Tadmor
Journal:
Math. Comp. 44 (1985), 361377
MSC:
Primary 65M10
MathSciNet review:
777269
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Abstract: New convenient stability criteria are provided in this paper for a large class of finitedifference approximations to initialboundary value problems associated with the hyperbolic system in the quarter plane , . Using the new criteria, stability is easily established for numerous combinations of wellknown basic schemes and boundary conditions, thus generalizing many special cases studied in the recent literature.
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G. Sköllermo, How the Boundary Conditions Affect the Stability and Accuracy of Some Implicit Methods for Hyperbolic Equations, Report No. 62, Dept. of Computer Science, Uppsala University, Uppsala, Sweden, 1975.
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G. Sköllermo, Error Analysis for the Mixed Initial Boundary Value Problem for Hyperbolic Equations, Report No. 63, Dept. of Computer Science, Uppsala University, Uppsala, Sweden, 1975.
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Eitan
Tadmor, The unconditional instability of
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(85a:65143), http://dx.doi.org/10.1090/S00255718198307176886
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E. Tadmor, SchemeIndependent Stability Criteria for Difference Approximations to Hyperbolic InitialBoundary Value Systems, Ph. D. Thesis, Department of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel, 1978.
 [16]
L. N. Trefethen, Wave Propagation and Stability for Finite Difference Schemes, Ph. D. Thesis, Report No. STANCS82905, Computer Science Department, Stanford University, Stanford, California, 1982.
 [1]
 M. Goldberg, "On a boundary extrapolation theorem by Kreiss," Math. Comp., v. 31, 1977, pp. 469477. MR 0443363 (56:1733)
 [2]
 M. Goldberg & E. Tadmor, "Schemeindependent stability criteria for difference approximations of hyperbolic initialboundary value problems. I," Math. Comp., v. 32, 1978, pp. 10971107. MR 501998 (80a:65196)
 [3]
 M. Goldberg & E. Tadmor, "Schemeindependent stability criteria for difference approximations of hyperbolic initialboundary value problems. II," Math. Comp., v. 36, 1981, pp. 603626. MR 606519 (83f:65142)
 [4]
 B. Gustafsson, "The convergence rate for difference approximations to mixed initial boundary value problems," Math. Comp., v. 29, 1975, pp. 396406. MR 0386296 (52:7154)
 [5]
 B. Gustafsson, H.O. Kreiss & A. Sundström, "Stability theory of difference approximations for mixed initialboundary value problems. II," Math. Comp., v. 26, 1972, pp. 649686. MR 0341888 (49:6634)
 [6]
 B. Gustafsson & J. Oliger, "Stable boundary approximations for implicit time discretizations for gas dynamics," SIAM J. Sci. Statist. Comput., v. 3, 1982, pp. 408421. MR 677095 (84c:65151)
 [7]
 A. Iserles & G. Strang, "The optimal accuracy of difference schemes," Trans. Amer. Math. Soc., v. 277, 1983, pp. 779803. MR 694388 (84f:65070)
 [8]
 H.O. Kreiss, "Difference approximations for hyperbolic difference equations," in Numerical Solutions of Partial Differential Equations (J. H. Bramble, ed.), Academic Press, New York, 1966, pp. 5158. MR 0207223 (34:7039)
 [9]
 H.O. Kreiss & J. Oliger, Methods for the Approximate Solution of Time Dependent Problems, GARP Publication Series No. 10, Geneva, 1973.
 [10]
 S. Osher, "Systems of difference equations with general homogeneous boundary conditions," Trans. Amer. Math. Soc., v. 137, 1969, pp. 177201. MR 0237982 (38:6259)
 [11]
 S. Osher, "Stability of parabolic difference approximations to certain mixed initialboundary value problems," Math. Comp., v. 26, 1972, pp. 1339. MR 0298990 (45:8039)
 [12]
 G. Sköllermo, How the Boundary Conditions Affect the Stability and Accuracy of Some Implicit Methods for Hyperbolic Equations, Report No. 62, Dept. of Computer Science, Uppsala University, Uppsala, Sweden, 1975.
 [13]
 G. Sköllermo, Error Analysis for the Mixed Initial Boundary Value Problem for Hyperbolic Equations, Report No. 63, Dept. of Computer Science, Uppsala University, Uppsala, Sweden, 1975.
 [14]
 E. Tadmor, "The unconditional instability of inflowdependent boundary conditions in difference approximations to hyperbolic systems," Math. Comp., v. 41, 1983, pp. 309319. MR 717688 (85a:65143)
 [15]
 E. Tadmor, SchemeIndependent Stability Criteria for Difference Approximations to Hyperbolic InitialBoundary Value Systems, Ph. D. Thesis, Department of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel, 1978.
 [16]
 L. N. Trefethen, Wave Propagation and Stability for Finite Difference Schemes, Ph. D. Thesis, Report No. STANCS82905, Computer Science Department, Stanford University, Stanford, California, 1982.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198507772697
PII:
S 00255718(1985)07772697
Article copyright:
© Copyright 1985
American Mathematical Society
